export animation to fbx or md2
On second read, I think I understand better. You are exporting a mesh with a modifier to an engine that doesn't support the same modifiers. Most realtime engines only support bone animations - a lot of them don't even support shape keys. 
Basically, you can't do what you are doing :)

You have a couple of options:

1: animate it in a way that doesn't use curve modifiers, only bones (might not be easy though)

2: save your mesh animation as an MDD (mesh cache) and load that into your engine, if possible.

3: See if you can set up an equivalent to a curve modifier in your engine. For example, you might be able to make a script that makes the wire traverse through a series of null points. This depends on the engine you are using though.